A New Mathematical Model for a Multi-depot Vehicle Routing Problem in a Natural Disaster Situation and Solving by a Particle Swarm Optimization Algorithm

Relief operation in a natural disaster situation is one of the applications of transportation problems. Transportation of the victims to the relief places such as hospitals, evacuation of afflicted areas is an important issue in the critical events, such as flood and earthquake. In this paper, a new mathematical model for a multi-depot vehicle routing problem is proposed that minimizes the earliest time of vehicles to the hospital depots. In this regard, vehicles are moved from started depots to critical places and then loaded the victims to take them to the hospitals. Afterwards in order to show its validation, the presented model is solved for smallsized problems by the Lingo software. Furthermore, it is solved for large-sized problems by particle swarm optimization (PSO) and improved PSO. Finally, the obtained results are compared and analyzed.